EDB — 0H9

[0H9] Topics:boundary.Difficulty:*.

Given \(X\) topological space and \(A⊆ X\); if \(A\) is open (or closed) the boundary \(∂ A\) has empty interior; we have \(∂ A⊇ ∂∂ A\) with equality if \(∂ A\) has empty interior; in addition \(∂∂ A= ∂∂∂ A\).